We call a linear code \(C\)  over \(\mathbb {F}_p\)  is minimal if all of its nonzero codewords are minimal. Further a codeword \(c\in C\)  is said to be minimal if \(supp(c^{\prime })\subseteq supp(c)\)  if and only if \(c^{\prime }=ac\) , where \(a(\ne 0)\in \mathbb {F}_p\) . In general, it is hard to determine whether a linear code is minimal or not but the famous Ashikhmin-Barg condition ([1]}) is a sufficient condition for a linear code to be minimal and it is relatively easy to check.
